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438

Bending Moment and Shear.

may be shewn to be parabolic, as at/s (Fig. 393), or greatest near
the axis, while on the contrary the  greatest  bending stress is
furthest from the axis, as shewn at A.
|/s x area of section = total shear

*~A f    s total shear load on section

ana js = -%---------------------:----------

area of section

In very short beams this stress should be considered, till
finally, in rivets and pins, the shear is almost pure. We will now
examine the distribution of Bending Moment and Shear Load
under various conditions of support arid load. (Seep. 922.)

I. Cantilever with Concentrated Load* (Fig. 394).—AB is
the beam and W the load, the latter having a leverage over

tJte= w

section A of W x / ton feet: at section D of W x f /, and so on.
The Bending Moments at various sections may therefore be repre-
sented on the base line ab by downward ordinates, thus :

AtA»W/xi      atD=W/xf

Atc=W/x|     atE=W/x^

and at B= nothing; and these ordinates are shewn at /^, hjr
and b.

The Shearing Force is caused by the reciprocal action of W and
Rt, and will equal W upon any section between A and B. For
regularity we shall always consider the force an the right side of

* Weight of beam is not taken, unless stated.